SKATE: Decoupling Systematic Sampling From Scoring · 2014. 10. 10. · SKATE: Decoupling Systematic Sampling From Scoring JIANWEN A. FENG, GARLAND R. MARSHALL Department of Biochemistry

SKATE: Decoupling Systematic Sampling From Scoring

JIANWEN A. FENG, GARLAND R. MARSHALL

Department of Biochemistry and Molecular Biophysics, Center for Computational Biology,Washington University School of Medicine, 660 S. Euclid Ave, St. Louis, Missouri 63110

Received 25 March 2009; Revised 16 February 2010; Accepted 21 February 2010DOI 10.1002/jcc.21545

Published online in Wiley InterScience (www.interscience.wiley.com).

Abstract: SKATE is a docking prototype that decouples systematic sampling from scoring. This novel approach

removes any interdependence between sampling and scoring functions to achieve better sampling and, thus,

improves docking accuracy. SKATE systematically samples a ligand’s conformational, rotational and translational

degrees of freedom, as constrained by a receptor pocket, to find sterically allowed poses. Efficient systematic sam-

pling is achieved by pruning the combinatorial tree using aggregate assembly, discriminant analysis, adaptive sam-

pling, radial sampling, and clustering. Because systematic sampling is decoupled from scoring, the poses generated by

SKATE can be ranked by any published, or in-house, scoring function. To test the performance of SKATE, ligands

from the Asetex/CDCC set, the Surflex set, and the Vertex set, a total of 266 complexes, were redocked to their re-

spective receptors. The results show that SKATE was able to sample poses within 2 A RMSD of the native structure

for 98, 95, and 98% of the cases in the Astex/CDCC, Surflex, and Vertex sets, respectively. Cross-docking accuracy of

SKATE was also assessed by docking 10 ligands to thymidine kinase and 73 ligands to cyclin-dependent kinase.

q 2010 Wiley Periodicals, Inc. J Comput Chem 00: 000–000, 2010

Key words: consensus scoring drug discovery; discriminant analysis; systematis search; virtual screening

IntroductionAQ2

Small molecule docking programs are used extensively in the

pharmaceutical industry and increasingly in academia for the

discovery of novel lead compounds. A number of docking pro-

grams are available either as commercial software or from aca-

demic labs.1-13 Molecular docking programs have three main

components: a representation of the system, a sampling algo-

rithm and a scoring function.14 A docking program must be able

to sample near-native poses to rank them as top-scoring poses.

A pose defines the relative orientation and conformation of a

ligand when bound to a receptor. Velec et al. noted that highly

accurate ligand poses (below 1 A root-mean-square deviation)

are a prerequisite to improving scoring functions.15

Evolutionary algorithms and other stochastic search methods

are common types of sampling algorithm. They rely on scoring

functions to guide their stochastic steps, so the search and scor-

ing processes are necessarily coupled. Scoring functions need to

evaluate anywhere from thousands to millions of poses in a

docking experiment. To speed up the calculations, the energy

functions are simplified so that they can be evaluated quickly.

The tradeoff is a less accurate energy function that at best

approximates the binding energy of a pose. If a coarse energy

function scores a near-native pose poorly, the pose will be dis-

carded. This problem of false negatives is often the root cause

of poor docking performance. The interdependence of sampling

and scoring in current docking programs makes it difficult to

determine whether a sampling error or a scoring error caused

poor performance in a docking experiment. SKATE is a novel

docking program that decouples systematic sampling from

imperfect scoring. It employs a rigorous search method to sys-

tematically sample conformational, orientation and rotational

degrees of freedom of a ligand to find optimal docking poses.

Any naive brute-force approach, literally rotating each bond,

results in combinatorial explosion and becomes computationally

intractable. In SKATE, efficient systematic sampling was

achieved by pruning the combinatorial tree using aggregate as-

sembly, discriminant analysis, adaptive sampling, radial sam-

pling and clustering. The resulting sterically allowed poses of a

ligand bound to a receptor were then ranked independently using

three scoring functions. The docking performance of SKATE

was evaluated by three large test sets in terms of self-docking,

and two test sets in terms of cross-docking.

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Correspondence to: G. R. Marshall; e-mail: [email protected]

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Overview of Docking sMethodology and Data Sets

Sampling

Hydrogen-bonding interactions are essential in drug specificity

and high affinity binding. SKATE takes advantage of this natural

phenomenon by forming all possible hydrogen-bond pairings

between the ligand and the receptor pocket to anchor systematic

search. Once a sterically allowed hydrogen bond is formed

between a receptor atom and a ligand atom, SKATE systemati-

cally samples the ligand’s torsional degrees of freedom. The

simplest systematic approach to find all sterically allowed con-

formations of a flexible ligand is to iteratively rotate each rotata-

ble bond. Assuming a ligand molecule of N atoms with T rotata-

ble bonds, and a receptor pocket of M atoms, if each rotatable

bond of the ligand is explored at angular increments of A

degrees, there are 360/A values to be examined for each T

resulting in (360/A)T possible conformations to be examined for

steric conflict. The 3D coordinates that determine the geometry

of a conformation can be generated by applying appropriate

transformation matrices to different subsets of atoms. These con-

formers must be checked for van der Waals (VDW) overlap to

eliminate sterically impossible conformations. To a first approxi-

mation, there are N(N-1)/2 pair-wise distance calculations that

must be performed for each conformation. Then M x N pair-

wise distance calculations must be performed between atoms in

each conformation and those in the receptor pocket. These dis-

tances are checked against the allowed sum of VDW radii for

the two atoms involved. The number of VDW comparison V for

a single hydrogen-bond formed between the receptor and the

ligand is given by V ¼ 360A

8: 9;T3

NðN�1Þ2þM3N

8: 9;. The rate-

limiting step in this brute force approach is the sheer number of

VDW comparisons that must be performed to find sterically

allowed poses. For example, sampling at torsional increments of

10 degrees for a ligand with 6 rotatable bonds and 50 atoms and

a receptor pocket of 1000 atoms will result in 1.4 e13 VDW cal-

culations. Assuming there is a combination of 50 possible hydro-

gen-bonds that can be formed, it would take 22 years to com-

plete this calculation on a modern, single CPU computer that is

capable of processing 1 million VDW comparisons per second.

Such a brute force approach to systematic search is obviously

both inefficient and unnecessary. SKATE implements a number

of strategies that truncate the combinatorial explosion. Sterically

allowed poses of a ligand as constrained by a receptor pocket

are systematically sampled by a step-wise build up of aggregates

(Fig. F11). An aggregate is defined as a set of atoms whose rela-

tive positions are invariant to rotational degrees of freedom.16 A

ligand is divided into individual aggregates around internal rotat-

able bonds (Fig. F22). An aggregate capable of hydrogen-bonding

is transformed by rigid-body translation and rotation to form an

energetically favorable hydrogen-bond with the receptor. The

geometries of the newly formed hydrogen-bond are determined

by a set of hydrogen-bonding geometric parameters. A second

aggregate that shares a common rotatable bond with the first ag-

gregate is spliced onto the partial molecule by applying the appro-

priate transformations. The range of sterically allowed torsions for

this rotatable bond is analytically determined by discriminant anal-

ysis.16 Discrete values in the range of allowed torsions are

sampled by rotating the second aggregate around the rotatable

bond that joins the first and second aggregates. The step-wise as-

sembly of sterically allowed conformations of the ligand within

the receptor pocket continues until all aggregates have been added.

As shown in Figure 1, the possible conformations of a flexible

ligand hydrogen-bonded to a receptor can be represented by a

search tree. The tree is anchored by a receptor atom that forms a

hydrogen bond with the ligand. SKATE systematically finds steri-

cally allowed ligand poses (tree leaves) by performing a depth-first

search of the tree. Systematic search is performed for each possi-

ble pairing of hydrogen-bonding atoms between the ligand and

receptor. A more detailed explanation of systematic search and

discriminant analysis is provided in the Methods section.



Figure 1. The tree structure of systematic search of conformational

space for a ligand hydrogen-bonded to a receptor. Vertices of the

tree represent ligand aggregates; edges represent discrete torsion val-

ues of a ligand’s rotatable bonds and a ligand-receptor hydrogen-

bond. Red edges represent ‘‘pruning’’ of the search tree by eliminat-

ing branches of the tree where the addition of an aggregate is steri-

cally prohibited for any torsion value. Sterically allowed conforma-

tions are represented by the tree leaves that are connected by black

edges. The first aggregate is hydrogen-bonded to the receptor and

the bonding geometries are determined from a set of geometric pa-

rameters. At each branch point, a new aggregate may be added to

the existing partial conformation if it is sterically allowed (black

lines). Each black line represents a torsion value of a rotatable bond

where an aggregate is added to the existing partial molecule. The as-

sembly of a sterically allowed conformation continues until aggre-

gates along every branch have been systematically evaluated. [Color

figure can be viewed in the online issue, which is available at

www.interscience.wiley.com.]AQ3

Figure 2. A simple molecule (left) is divided into its aggregates

(right) by partition at its rotatable bonds.

2 Feng and Marshall • Vol. 00, No. 00 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

Scoring

SKATE decouples systematic sampling from scoring. A unique

feature of SKATE is that any scoring function may be used to

rank the ensemble of poses generated by SKATE. SKATE itself

does not use a scoring function per se to determine if a pose is

low energy, but relies on a calibrated set of VDW radii and the

assumption of a hydrogen bond with a set of defining parameters.

It uses discriminant analysis and incremental build-up of the

ligand to find the set of sterically allowed poses. Those poses are

clustered with a heavy atom root-mean-square deviation (RMSD)

cutoff of 0.5 A. In this work, we used energy functions in

FRED,17 Rosetta6 and X-Score18 to rank or score the poses gener-

ated by SKATE. These scoring functions are made available by

their respective authors at no charge to academic groups.

FRED or Fast Rigid Exhaustive Docking is a commercial dock-

ing program developed by OpenEye that can also be used to score

poses generated by other programs.17 We used FRED’s default con-

sensus scoring function that is an equal-weighted sum of ranks by

chemgauss3, PLP, and oechemscore. Chemgauss3 uses smooth

Gaussian functions to represent the shape and chemistry of mole-

cules.17 PLP, or Piecewise Linear Potential, is a minimal scoring

function that includes a steric term and a hydrogen-bonding term,

but no electrostatic term.19 Oechemscore is an OpenEye variant of

chemscore, an empirical scoring function.20 We also examined how

FRED scoring is affected by a fast, rigid-body local optimization of

SKATE-generated poses before scoring.

Rosetta’s energy function was originally trained for protein

structure prediction and was extended to score protein-ligand

interactions.15 The energy function consists of a weighted sum

of force-field-based and knowledge-based terms calculated from

the receptor and ligand coordinates. Hydrogen atoms are explic-

itly treated. The terms include VDW interactions, an implicit

solvent model, an explicit orientation-dependent hydrogen-bond-

ing potential, and an electrostatics model. For this work, we

used Rosetta’s energy function, referred to as Rosetta-Score, to

rank poses generated by SKATE.

X-Score is an empirical scoring function that treats hydro-

phobic effect by using three different functions and averaging

the results.18 Each of the three functions includes a VDW inter-

action term, a hydrogen-bonding term, a hydrophobic effect

term, a torsional-entropy penalty, and a regression constant.

X-score was trained to reproduce the known binding affinity of

200 protein-ligand complexes.

Data Sets

SKATE was tested on five data sets in assessing its self-docking and

cross-docking performance. Results from four of the data sets can

be compared directly to results from published docking programs.

Astex/CCDC Diverse Set

Hartshorn et al. prepared a set of 85 high-quality and diverse

protein-ligand complexes and made them publicly available as a

validation set for testing docking performance.21 Protein targets

were selected based on their relevance to drug discovery or

agrochemical research. Consequently, only complexes with

drug-like ligands were allowed in this set. To ensure complex

diversity, no receptor was represented more than once. Further-

more, the ligands contained distinct molecular recognition types.

A special focus was placed on selecting very high-quality exper-

imental structures for which the experimental binding mode of

the ligands was easily assessed. Protein structures were prepared

by removing solvents and small ions. Exceptions were made for

water molecules that coordinate a metal ion and for small ions

that mimic a cofactor. His, Asn and Gln side-chain placements

in the crystal structure that were not consistent with hydrogen-

bonding patterns were rotated if such rotations would signifi-

cantly improve hydrogen-bonding. This is reasonable because

crystallographers usually cannot orient His, Asn, and Gln side

chains with absolute certainty based on electron density alone.

This data set was downloaded from the Cambridge Crystallo-

graphic Data Centre (http://www.ccdc.cam.ac.uk).

Surflex Set

To compile a test set for Surflex, Jain filtered 134 protein-ligand

complexes in the GOLD data set by removing complexes that

(i) contained ligands with more than 15 rotatable bonds, (ii)

were covalently attached to the protein, and (iii) contained

obvious errors in structure.1,22 The resulting 81 complexes were

made available on http://jainlab.ucsf.edu. The protein files in the

original GOLD set were prepared by removing water molecules

and by adding hydrogen atoms while taking protonation states

into account. Exceptions were made to keep water molecules

and metal atoms that coordinated ligand binding.1

Vertex Set

Perola et al. prepared a test set of 150 protein-ligand complexes

to compare the performances of Glide, GOLD and ICM.23 These

complexes were selected for their relevance to modern drug dis-

covery programs. Ligands were selected for (i) their drug-like

properties; (ii) molecular weights between 200 and 600 Daltons;

(iii) having between 1 and 12 rotatable bonds; and (iv) structural

diversity. The ligands in the Vertex set were prepared by

extracting them from their respective PDB files and assigning

bond orders and correct protonation states by visual inspection.

Protein structures were prepared by removing subunits, ions, sol-

vent and other small molecules not involved in binding. Metal

ions and tightly bound water molecules in the ligand binding

site were preserved.23 Hydrogen atoms were added to the pro-

tein. The structures of ligand, protein, and cofactor were mini-

mized as a complex for 1,000 steps using Macromodel and the

OPLS-AA force field. All heavy atoms were constrained to their

original positions during minimization. The structures with opti-

mized hydrogen positions were saved. Of the 150 complexes,

100 are PDB entries and 50 are corporate structures. The files of

the 100 PDB complexes are available on the Jain Lab website

(http://jainlab.ucsf.edu).10 Seven complexes in the Vertex set are

also included in either the Astex/CDCC set or the Surflex set

(Table T11).

Thymidine Kinase Set

Bissantz et al. tested the virtual screening capability of docking

programs by using the crystal structure of HSV-1 thymidine ki-



3SKATE: Decoupling Systematic Sampling from Scoring AQ1




Table 1. Results for Skate on the Astex/CDCC, Surflex and Vertex complexes.a

Vertex Set Astex/CDCC set Surflex set

RMSD RMSD RMSD

PDB code nrot Best pose Top rank PDB code nrot Best pose Top rank PDB code nrot Best pose Top rank

13gs 3 0.49 0.83 1g9v 5 1.49 1.51 1abe 0 0.45 0.45

1a42 8 0.77 1.41 1gkc 8 1.27 0.95 1acj 1 0.46 0.68

1a4k 5 0.66 1.81 1gm8 4 1.59 2.24 1ack 2 0.53 3.83

1a8t 8 1.00 7.99 1gpk 1 0.27 0.30 1acm 6 0.70 0.65

1afq 9 0.86 8.23 1hnn 1 0.67 0.98 1aco 2 0.27 0.35

1aoe 3 0.48 0.86 1hp0 2 0.45 0.36 1aha 0 0.26 0.18

1atlb 8 0.91 1.26 1hq2 1 0.43 0.26 1atl 9 1.35 2.86

1azm 2 0.51 1.28 1hvy 8 1.77 1.64 1baf 4 0.64 0.92

1bnw 5 0.64 5.48 1hwi 9 0.61 1.11 1bbp 9 0.75 0.76

1bqo 6 0.30 0.48 1hww 1 0.22 0.14 1bma 9 1.65 2.47

1br6 3 0.39 1.14 1ia1 2 0.26 0.36 1cbs 0 0.20 0.36

1cet 7 0.93 7.45 1ig3 4 0.44 1.20 1cbx 5 0.29 0.43

1cim 3 0.28 1.09 1j3j 2 0.18 0.30 1com 4 0.46 0.79

1d3p 12 1.14 1.19 1jd0 1 0.72 3.36 1coy 1 0.32 0.51

1d4p 3 0.24 0.60 1jje 7 0.58 7.97 1dbb 1 0.25 0.51

1d6v 7 0.92 2.17 1jla 7 0.70 0.77 1dbj 1 0.32 0.54

1dib 7 0.80 2.88 1k3u 6 0.27 0.29 1dr1 3 0.28 1.48

1dlr 4 0.42 0.64 1ke5 1 0.34 0.29 1dwd 8 1.16 2.97

1efy 3 0.42 1.76 1kzk 9 0.65 0.89 1eap 10 0.82 0.81

1ela 8 0.44 0.68 1l2s 2 0.31 0.51 1epb 0 0.91 0.74

1etrb 8 0.46 0.60 1l7f 8 0.33 0.44 1etr 8 0.92 0.93

1ett 6 0.51 0.98 1lpz 6 0.71 1.00 1fend 0 – –

1eve 6 1.38 1.01 1lrh 2 1.32 1.42 1fkg 9 0.78 1.60

1exa 4 0.25 0.32 1m2z 3 0.19 0.60 1fki 0 0.30 0.34

1ezq 10 0.39 0.71 1meh 7 1.12 1.07 1frp 7 0.26 0.92

1f0r 4 0.40 0.75 1mmv 8 0.81 0.58 1glq 12 1.62 9.14

1f0t 5 0.73 2.57 1mzc 7 1.27 2.26 1hdc 6 1.41 1.61

1f4e 2 0.41 1.09 1n1m 3 0.82 0.57 1hdy 0 0.90 0.74

1f4f 8 0.67 2.23 1n2j 4 0.67 0.47 1hri 9 2.87 10.18

1f4g 11 1.23 1.49 1n2v 3 0.45 1.08 1hsl 4 0.36 0.42

1fcx 4 0.28 0.32 1n46 5 0.43 0.66 1hyt 5 0.65 0.78

1fcz 3 0.26 0.39 1nav 5 0.39 0.73 1lah 6 0.36 0.36

1fjs 8 1.16 2.01 1of1 2 0.32 0.32 1lcp 4 0.56 1.13

1fkgb 9 0.64 1.33 1of6 4 0.32 0.64 1ldm 0 0.18 0.39

1fm6 6 0.68 0.74 1opk 2 0.35 0.56 1lic 15 5.05 5.07

1fm9 11 0.48 2.31 1oq5 3 0.37 5.00 1lna 10 0.64 0.74

1frb 5 0.24 0.23 1owe 2 1.01 1.84 1lpm 8 0.89 6.82

1g4o 5 1.04 3.59 1oyt 4 0.40 0.62 1lst 7 0.29 0.21

1gwx 10 1.61 2.19 1p2y 1 1.67 4.87 1mdr 3 0.20 0.47

1h1p 3 0.43 0.43 1p62 3 0.16 0.40 1mrg 0 0.29 0.59

1h1s 4 0.46 0.66 1pmn 6 2.51 6.70 1mrk 3 0.36 0.99

1h9u 3 0.26 0.39 1q1g 3 0.36 0.69 1nco 9 0.91 0.68

1hdq 5 0.98 1.03 1q41 1 0.34 0.54 1phg 3 0.87 4.39

1hfc 10 0.60 0.52 1q4g 3 0.27 0.64 1rds 8 1.03 1.74

1hpv 12 0.88 0.89 1r1h 10 0.43 0.53 1rob 5 0.94 1.41

1htf 13 0.92 2.10 1r55 8 0.98 0.86 1snc 6 0.54 0.80

1i7z 5 0.39 0.48 1r58 9 0.77 0.91 1srj 2 0.40 0.40

1i8z 6 4.82 4.80 1r9o 3 0.52 0.76 1stp 5 0.40 0.79

1if7 7 0.88 5.13 1s19 5 0.38 0.62 1tka 8 1.21 1.46

1iy7 5 0.30 0.64 1s3v 5 0.38 0.73 1tmn 13 0.75 1.48

1jsv 1 0.46 0.39 1sg0 3 0.32 0.49 1tng 2 0.10 0.69

1k1j 8 0.45 1.61 1sj0 6 0.54 0.66 1tni 5 0.57 1.92

1k22 9 0.42 0.49 1sq5 6 0.81 1.68 1tnl 2 0.19 0.40

(continued)





Table 1. (Continued).

Vertex Set Astex/CDCC set Surflex set

RMSD RMSD RMSD

PDB code nrot Best pose Top rank PDB code nrot Best pose Top rank PDB code nrot Best pose Top rank

1k7e 4 0.18 1.00 1sqn 2 0.22 0.27 1trk 9 0.40 0.58

1k7f 5 0.66 1.20 1t40 6 0.65 0.69 1ukz 4 0.20 0.24

1kv1 1 0.24 0.81 1t46 4 0.43 0.38 1ulb 0 0.20 0.46

1kv2 6 0.53 0.55 1t9b 3 0.61 0.47 1wap 4 0.17 0.32

1l2sc 1 0.17 0.42 1tow 4 0.56 4.81 2ada 3 0.15 0.19

1l8g 3 0.33 2.13 1tt1 4 0.29 0.73 2ak3 4 0.42 0.55

1lqd 5 0.56 1.00 1tz8 5 0.58 2.29 2cgr 5 1.66 1.80

1m48 7 0.56 0.96 1u1c 6 0.60 1.12 2cht 3 0.67 1.36

1mmb 13 0.82 6.79 1u4d 1 0.28 0.91 2cmd 6 0.57 0.45

1mnc 10 0.80 1.55 1uml 9 0.54 0.62 2ctc 4 0.24 0.41

1mq5 3 0.26 0.41 1unl 6 0.55 0.95 2dbl 6 1.62 1.35

1mq6 4 0.27 0.32 1uou 2 0.73 0.73 2gbp 2 0.19 0.26

1nhu 8 0.44 0.46 1v0p 6 0.50 0.45 2lgs 5 1.13 1.74

1nhv 8 1.15 7.46 1v48 6 0.45 0.35 2phh 2 0.25 0.41

1o86 12 7.97 8.63 1v4s 3 0.29 0.28 2r07 8 1.64 8.96

1ohr 11 0.39 0.46 1vcj 8 0.59 0.84 2sim 5 0.40 1.21

1ppc 8 1.08 1.96 1w1p 0 0.24 0.28 3aah 3 0.79 0.39

1pph 6 0.76 2.03 1w2g 2 0.39 0.56 3cpa 6 0.88 0.92

1qbu 10 0.72 0.77 1x8x 4 0.44 0.78 3hvt 1 2.33 1.62

1qhi 4 0.25 0.40 1xm6 5 0.53 1.23 3ptb 1 0.23 0.42

1ql9 3 0.37 0.37 1xoq 5 0.95 4.03 3tpi 7 0.26 0.26

1qpe 2 0.42 0.55 1xoz 1 0.26 0.28 4cts 2 0.27 0.44

1r09 3 0.75 0.60 1y6b 6 0.39 0.34 4dfr 8 0.84 1.19

1syn 7 0.59 2.48 1ygc 10 2.55 3.85 6abp 1 0.34 0.39

1thl 11 0.82 0.95 1yqy 4 0.18 0.51 6rnt 4 0.38 7.01

1uvs 8 1.30 1.49 1yv3 2 0.30 0.31 6rsa 2 0.47 0.76

1uvt 5 0.49 0.45 1yvf 4 0.58 0.60 7tim 3 0.47 1.13

1ydr 1 0.36 0.36 1ywr 5 0.54 0.45 8gch 8 1.56 2.20

1yds 4 0.44 0.37 1z95 5 0.31 0.34

1ydt 7 0.87 3.46 2bm2 7 0.45 1.48

2cgrb 5 0.60 0.78 2br1 6 1.12 1.58

2csn 4 1.54 3.01 2bsm 6 0.50 0.74

2pcp 2 0.24 0.30

2qwi 5 0.24 1.01

3cpab 7 0.45 1.07

3erk 3 0.25 0.60

3ert 8 0.48 1.03

3std 5 0.26 0.26

3tmn 6 0.47 0.71

4dfrb 8 0.98 1.42

4std 4 0.26 0.35

5std 4 0.52 0.32

5tln 9 0.80 1.06

7dfr 8 0.77 1.44

7est 6 0.43 0.82

830c 7 0.29 0.52

966c 7 0.30 0.63

aTop rank poses are scored by FRED-Opt-Score.bComplex is also part of the Surflex set.cComplex is also part of the Astex/CDCC set.dThe ligand in complex 1fen does not have any atom that is capable of hydrogen bonding.



nase (TK) (PDB ID: 1KIM), 10 known ligands, and 990 ran-

domly chosen decoys.24 In this work, the 10 known ligands

were docked to the 1KIM structure to test SKATE’s perform-

ance in cross-docking. The structures were prepared as described

in Bissantz et al. No optimization of ligand or receptor coordi-

nates was performed.

Cyclin-Dependent Kinase 2 Set

Seventy-three known ligands that have been cocrystallized with

cyclin-dependent kinase 2 (CDK2) were docked to a single high

resolution CDK2 structure (PDB ID: 2B54, 1.85 A).25 These

ligands occupy the ATP-binding site of CDK2. To prepare the re-

ceptor, water molecules and cocrystallized ligands were removed

from the 2B54 structure, and hydrogen atoms were added to the

receptor using Sybyl 8.1.26 The ligand structures were extracted

from their respective complexes, and were assigned correct bond

orders and protonation states by visual inspection. To create refer-

ence coordinates of the 73 known ligands, their respective cocrys-

tallized receptors were aligned to the 2B54 structure and the

ligands were extracted and saved as mol2 files.

Docking Setup

The files in the Astex/CDCC, Surflex and Vertex sets were

downloaded from their respective websites and used as obtained.

Hydrogen atoms were already added to protein and ligand struc-

tures by the test sets’ respective authors. No further optimization

of protein or ligand geometries were performed since it could

lead to biased results.27 For the Vertex set, its author did mini-

mize the ligand and receptor hydrogen atoms while constraining

the heavy atoms to their original locations.23 Ligand and protein

files in PDB or MOL formats were converted to the mol2 format

and assigned Tripos atom types. The coordinates of these ligand

files were used as references when calculating RMSD values.

In this study, the experimentally determined ligand was used

to define the binding pocket for the purpose of docking. A list

of potential hydrogen-bond donors and acceptors were created

by inspecting the receptor atoms that are within 5 A of the coc-

rystallized ligand. The coordinates from this list of atoms served

as anchor points in systematic search. SKATE attempted to dock

all possible pairings of ligand hydrogen-bond donors with pro-

tein hydrogen-bond acceptors, and vice versa. A vast majority of

these attempted pairings resulted in immediate search termina-

tion because they were not sterically allowed. The resulting

sterically allowed poses generated by SKATE were written to a

file in the mol2 format to be ranked by scoring functions.

Results and Discussion

Sampling Accuracy

To rank a near native pose as the top-scoring pose, a docking

program must be able to sample such poses. The interdepend-

ence of sampling and scoring in current docking programs

makes it difficult to determine whether it is a sampling error or

a scoring error that caused a program to fail on a given test

case. SKATE approaches the docking problem by decoupling

systematic sampling from scoring. It anchors a search by pairing

a ligand hydrogen-bond donor to a receptor hydrogen-bond

acceptor and vice versa. For each hydrogen-bond formed,

SKATE systematically samples a ligand’s torsional degrees of

freedom to find poses that sterically fit within a receptor pocket.

To delete conformational memory of the experimentally deter-

mined ligand structures, their torsions were reset to 180 degrees

before docking. Bond angles, bond lengths and ring conforma-

tions were not modified. Receptor atoms within 5 A of the coc-

rystallized ligand defined the binding pocket. Figure F33 shows the

cumulative proportion of best poses, as measured by RMSD to

the experimental structure (reference), that were generated by

SKATE for the complexes in the Astec/CDCC, Surflex and Ver-

tex self-docking test sets. A pose is considered best if its heavy

atom RMSD to the reference structure is the lowest. Table 1

lists the RMSD values of the best poses and top-scoring poses

for each complex in the three test sets. For an RMSD threshold

of 2 A, sampling accuracy rates are 98, 95, and 98% for the

Astex/CDCC, Surflex and Vertex sets, respectively. For an

RMSD threshold of 1 A, the respective sampling accuracy rates

are 86, 80, and 88% for the three self-docking sets. Highly accu-

rate ligand poses that approximate the native pose below 1 A

RMSD are a prerequisite to improving solutions to the scoring

problem.15 For all but a few test cases in the three test sets,

SKATE was able to sample poses that were within 2 A. The

highly accurate sampling of SKATE can be attributed to the sys-

tematic sampling algorithm. It is essential for a docking program

to sample near-native poses of the complex to give scoring func-

tions the opportunity to rank them as top-scoring poses.

Systematic sampling in SKATE never repeatedly samples the

same point in conformational space. In practice, two conforma-

tions can be clustered when their only difference is a 10 degree

torsional variation in a terminal rotatable bond. To speed up

sampling, SKATE implements heuristics to further reduce con-

formational space. As shown in Figure 1, the possible conforma-



Figure 3. Cumulative proportion of best RMSD poses for the

Astex/CDCC (red), Suflex (green), and Vertex (blue) sets. There are

85 complexes in the Astex/CDCC set, 81 complexes in the Surflex

set and 100 complexes in the Vertex set. [Color figure can be

viewed in the online issue, which is available at www.interscience.

wiley.com.]



tions of a ligand that is hydrogen-bonded to a receptor can be

represented by a search tree. The edges, nodes, and leaves of the

tree represent torsion values of rotatable bonds, aggregates and

sterically allowed poses, respectively. SKATE traverses this tree

using a depth-first search approach. Upon reaching a leaf of the

tree by traversing down a branch from the root, a sterically

allowed conformation is found. SKATE determines if it is neces-

sary to travel down a branch of the tree by checking if the par-

tial ligand constructed thus far is similar to a ligand pose that

was already found from visiting previous tree branches. If the

RMSD between atoms in a partial ligand and the corresponding

atoms in a previously generated pose is less than 0.3 A, then

SKATE terminates the search of the current branch. If the search

were to be continued, the resulting poses would be very similar

to the previously generated pose and would be discarded during

clustering.

Discriminant analysis determines the range of torsions that

are sterically allowed for a rotatable bond. The allowed range of

torsions is discretized and converted into a list of torsions to be

sampled. Not all conformers assembled from this list of values

will be low in energy. Ligands in the receptor-bound state rarely

adopt strained conformations where the torsions of rotatable

bonds deviate significantly from the energy minima of the

1gauche, -gauche, and anti rotations. SKATE truncates confor-

mational space by limiting allowed torsions to be within 30

degrees of 1gauche, -gauche and anti torsions for rotatable

bonds that (i) are not terminated by oxygen or sulfur atoms, and

(ii) contain atoms that are bonded to fewer than four heavy

atoms. For terminal aggregates of a ligand, only the three tor-

sions that are nearest to 1gauche, -gauche and antivalues are

sampled for rotatable bonds that meet the above criteria (i) and

(ii). SKATE uses a combination of 180 geometric parameters to

predict potential hydrogen-bonding interactions between a ligand

acceptor and receptor donor, and vice versa. The parameters that

represent the most common geometries are tried first. SKATE

skips the remaining parameters if a pose is found. These heuris-

tics that reduce the search space to speed up performance are

optional and can be enabled or disabled by the user.

Analysis of Failed Sampling Cases

SKATE was able to sample a pose that is within 2 A RMSD of

the reference structure for 98, 95, and 98% of the test cases in

the Astex/CDCC, Surflex, and Vertex data sets, respectively.

Two of the ligands in the 85 complexes Astex/CDCC set barely

missed the 2 A RMSD threshold; their RMSD values were 2.51

and 2.55. SKATE was unable to sample a pose that was within

2 A RMSD of the native structure for test cases 1O86 and 1I8Z

in the Vertex set. In 1O86, lisinopril, an antihypertension drug,

is bound to the human angiotensin converting enzyme (ACE).

There are 12 rotatable bonds in lisinopril. The ACE active site

consists of a zinc-coordinated narrow groove flanked by two

large hydrophobic pockets. Poses found by SKATE occupied ei-

ther one of the pockets exclusively but were not able to bridge

the two. To correctly dock lisinopril to ACE, a docking program

must sample a pose where the carboxyl group of lisinopril cor-

rectly coordinates the zinc atom and still fits sterically into a

very narrow channel. For test case 1I8Z, the ligand also coordi-

nates a zinc atom, but SKATE failed to generate a pose that

captured this interaction. For the Surflex set, SKATE failed to

find near-native poses for 1FEN, 1HRI, 1LIC, and 3HVT. The

1FEN ligand does not have any hydrogen-bonding atoms and

SKATE could not anchor its search since it could not form a

hydrogen bond between the ligand and the receptor. For 1HRI,

the ligand does not form a hydrogen bond with the receptor.

SKATE sampled a pose (RMSD 5 2.87 A) where the ligand did

form a hydrogen bond with the receptor but its orientation was

inverted. Similarly, the 3HVT ligand does not form a hydrogen

bond with its receptor and the best pose RMSD value was 2.33 A.

The 1LIC ligand is a simple alkyl chain molecule that has 15

rotatable bonds; it is a poor candidate for testing docking pro-

grams because it does not represent drug- or lead-like com-

pounds and should not have been included in the Surflex test

set. For the Astex/CDCC and the Vertex sets, SKATE sampled

near-native poses (�2.0 A) for 98% of the test cases. Ligands in

the Astex/CDCC were selected for an unambiguous fit to the ex-

perimental electron density. Protons in the Vertex set were opti-

mized to alleviate poor steric contacts. The likelihood of inter-

molecular penetration of VDW surfaces in these two test sets is

lower because of high structural resolution in one case and pro-

ton optimization in another.

PDB structures are static models that best fit the available

electron density data. Errors in lower resolution structures may

result in poor modeling of small molecule ligands. This could

lead to poor intermolecular steric contacts and even incorrect fit-

ting of the electron density.28 It is important to keep this in

mind when assessing a docking program’s ability to reproduce

experimentally determined ligand poses.

Scoring Accuracy

SKATE focuses on the systematic sampling of sterically allowed

poses of a ligand where its search space is constrained by a

binding pocket. It does not provide a scoring function to rank

order the generated poses per se, but takes advantage of the

many published scoring functions’ ability to rerank docked

poses. In this article, we presented data from using X-Score,

Rosetta, and FRED energy functions to rank SKATE-generated

poses. X-Score is an empirical scoring function that estimates

the hydrophobic effect by using three different functions and

averaging the results.18 Rosetta’s energy function was originally

trained for protein-structure prediction and was extended to

score protein-ligand interactions.15 In this article, Rosetta’s

energy function will be referred to as Rosetta-Score. FRED17

itself is a docking program, but could also be used to rank previ-

ously generated poses with a consensus scoring function that

consists of chemgauss3, PLP, and oechemscore. It will be

referred to as FRED-Score.

We also evaluated whether rigid-body, local optimization of

SKATE-generated poses would improve overall docking per-

formance. SKATE allows some VDW penetration by scaling

atomic VDW radii within the systematic sampling algorithm

(see methods section for details). FRED’s consensus scoring

function could rank a near native pose poorly due to poor con-

tacts. Before scoring, poses were optimized by performing fast,

small-scale, rigid-body translations (0.75 A) or rotations (0.5 A),





a total of 72 systematic transformations, using FRED.17 The

optimized pose was selected by using the PLP scoring function.

The receptor atoms were fixed throughout the optimization pro-

cess. We emphasize that we only used the rigid-body, local opti-

mization feature of FRED, not its full-fledged docking capabil-

ities. The process of optimizing and scoring with FRED will be

referred to as FRED-Opt-Score.

The results of using X-score, Rosetta-Score, FRED-Score,

and FRED-Opt-Score to rank SKATE-generated poses for the

Astex/CDCC test set are shown in Figure F44A. For an RMSD

threshold of 2.0 A, the success rates were 87%, 85%, 73%, and

66% for FRED-Opt-Score, FRED-Score, Rosetta-Score and

X-Score, respectively. SKATE coupled with FRED-Opt-Score

ranking performed particularly well in identifying poses that

were less than 1 A RMSD as the best pose for the Astex/CDCC

set. Its accuracy rate was 72%. This is very encouraging because

only 86% of the test cases had a pose that was less than 1 A

RMSD. Taking that into account, the scoring accuracy rate is

84% for ranking a pose that is within 1 A RMSD from the

native structure. This could partly be attributed to the high qual-

ity of the x-ray structures comprising the Astex/CDCC set.

Similar to the results in the Astex/CDCC set, FRED-Opt-

Score performed best in identifying poses that were within 2 A

RMSD as the best pose for the Surflex set. FRED-Opt-Score’s

accuracy rate was 84% (Fig. 4B). FRED-Score, X-Score and

Rosetta-Score’s accuracy rates were 75%, 64%, and 52%,

respectively.

The results for the Vertex test set are shown in Figure 4C.

For an RMSD threshold of 2.0 A, the success rates were 77%,

73, 70, and 69% for FRED-Opt-Score, FRED-Score, Rosetta-

Score and X-Score, respectively. For an RMSD threshold of

1 A, the scoring accuracy of FRED-Opt-Score was 53% and that

of FRED-Score was 50%. The performance of FRED-Score and

that of FRED-Opt-Score were comparable in identifying a pose

that is within 1 A RMSD as the best pose.

Existing literature that evaluates docking program performan-

ces usually focuses on overall docking results such as the frac-

tion of correctly predicted protein-bound conformations.23,29

However, this kind of comparison is not conducive to pinpoint-

ing the cause of poor performance, i.e. whether poor perform-

ance is attributable to poor sampling, inaccurate scoring or both,

thereby making it difficult to isolate and fix problem areas. In

this work, the same set of high quality SKATE-generated poses

was ranked by FRED-Score, X-Score, and Rosetta-Score.

Because the sampling and the scoring were separated, it allowed

for a fair comparison of the scoring function performances.30

Although comparing scoring performance is not the main pur-

pose of this work, it is still valuable to discuss the results. In all

three self-docking test sets, FRED-Score was the most accurate

scoring function (Fig. 4). FRED-Score summed the individual

ranks by chemgauss3, PLP, and oechemscore to produce a con-

sensus rank. This ‘‘rank-by-rank’’ strategy was also employed by

Wang et al. in a study evaluating consensus scoring functions.30

They showed that combining results from three complementary

scoring functions improved the recognition of near-native poses

(� 2.0 A) as best poses. Coincidently or not, FRED-Score and

one of the best consensus functions in Wang et al. both included

the PLP scoring function. Rosetta-Score is an extension of



Figure 4. Cumulative proportion of top scoring RMSD for 85 com-

plexes in the Astex/CDCC set (A), 81 complexes in the Surflex set

(B) and 100 complexes in the Vertex set (C). Poses were generated

by SKATE and were ranked by X-Score(red), Rosetta-Score (green),

FRED-Score (blue), and FRED-Opt-Score (magenta). [Color figure

can be viewed in the online issue, which is available at www.

interscience.wiley.com.]



Rosetta’s energy function which was designed for in silico pro-

tein structure prediction. It may not have been optimally para-

meterized to score protein-ligand interactions. X-score was suc-

cessful in ranking a pose that is within 2 A of the experimental

conformation in the range of 64–69% for the three test sets.

This is consistent with a 66% success rate observed by Wang

et al. in evaluating X-score on a 100 complexes test set.30

Generally, rigid-body local optimization of SKATE-generated

poses improved FRED scoring. At RMSD thresholds between 1

and 2 A, optimization followed by FRED scoring improved ac-

curacy by up to nine percentage points. Poses with RMSD val-

ues under 2 A are often considered near-native but some may

contain poor contacts that cause a scoring function to rank them

poorly. A quick rigid-body local optimization or minimization of

those poses alleviated those poor contacts and resulted in better

scores. PLP was the scoring function used in the rigid-body opti-

mization of SKATE poses. Despite its simplicity, PLP has been

shown to be one of the top performing scoring functions and is

incorporated in multiple docking programs.12,19,30 Results from

using oechemscore or chemgauss3 as the scoring function for

optimization were similar to those from using PLP.

Examples of Scoring Errors

The best poses for the 1JJE and 1OQ5 complexes in the Astex/

CDCC were 0.52 A and 0.37 A, respectively. However, the

RMSD of the top-scoring pose, ranked by FRED-Opt-Score, for

1JJE was 7.97 A and that for 1OQ5 was 5.00 A. Upon closer

inspection of the 1JJE poses, we found the shapes of the top

scoring pose and the native pose were essentially superimpos-

able. The middle parts of the two poses overlap very well but

the two ring systems on the ligand were placed in opposite ori-

entations in the top-scoring pose (Fig.F5 5). Due to the symmetric

nature of this ligand, this was a challenging case for scoring,

because a small difference in 3D docked shape may be ‘‘flipped’’

to yield a large apparent RMSD. FRED-Score, X-Score and

Rosetta-Score also failed to rank a near-native pose as the top-

scoring pose. 1OQ5 is another example where the shapes of the

top-scoring pose overlapped well with the native pose (Fig.F6 6).

A phenyl group was swapped with a trichloromethyl group in

the top-scoring pose. FRED-Score, X-Score and Rosetta-Score

also failed to rank a near-native pose as the top-scoring pose.

Comparison with Other Docking Programs

Directly comparable docking results for the Astex/CDCC set are

available for GOLD.1 The success rate for GOLD21 was 81%

(Fig.F7 7A); which was 6% lower than SKATE. GOLD and

SKATE used the crystallographically determined ligand bond

angles and bond lengths. GOLD does allow ring flipping while

SKATE does not sample ring flexibility. GOLD defined its bind-

ing site as all protein atoms within 6 A of a nonhydrogen ligand

atom. SKATE defined its binding site as all protein atoms within

5 A of hydrogen and nonhydrogen ligand atoms. The two bind-

ing sites are nearly identical because the hydrogen-heavy atom

bond-length is 1 A.

Seventy-seven of 81 complexes in the Surflex set were

docked by the authors of Glide.11 Glide’s success rate for this

subset was 82% for an RMSD threshold of 2.0 A. The same

subset was also docked by the authors of MolDock12 with a

resulting success rate of 87%. For comparison, the success rate

of Surflex22 was 77% and that of SKATE/FRED-Opt-Score was

73% for the entire set of 81 complexes (Fig. 7B). The energy

minimized ligands, with torsions set to 180, were the input

structures for SKATE. SKATE’s systematic sampling was anch-

ored by pairing H-bond donors and acceptors between the ligand

and receptor H-bond atoms (defined in docking setup), and the

ligand was allowed to sample regions outside of this 5 A radius.

It is hard to directly compare the results of Glide, MolDock,

Surflex, and SKATE for several reasons. First, Glide and Mol-

Dock’s success rates are based on 77 complexes, a subset of the

81 complexes in Surflex. Both Suflex and SKATE’s success

rates are based on the entire 81 complexes in the Surflex set.

Second, MolDock basically trained its scoring function on this

set of 77 complexes as pointed out by Hawkins et al.28 Third,

Glide calculated RMSD using optimized ligand coordinates

instead of experimentally determined coordinates. Glide also

used the optimized ligand and protein coordinates in its docking

setup. The fact that the same energy function, OPLS/AA, was

used in both complex optimization and pose scoring means

Glide biased its methods by guaranteeing that the initial coordi-

nates were at a local energy minimum per the OPLS/AA scoring

function.10,11,13,28



Figure 5. The RMSD between the 1JJE native pose (blue) and top-

scoring pose (gray) of the ligand was 7.97 A. The two ring systems

of the top scoring pose were oriented in opposite directions.

Figure 6. The RMSD between the 1OQ5 native pose (blue) and

top-scoring pose (gray) was 5.00 A. A phenyl group was swapped

with a trichloromethyl group in the top-scoring pose.

COLOR

COLOR



Perola et al.23 prepared a test set of 150 protein-ligand com-

plexes to compare the performances of Glide, GOLD and ICM.

Of the 100 publicly available PDB structures, Glide correctly

identified a docked pose that was within 2.0 A RMSD of the ex-

perimental structure in 59% of the cases, versus 48% by GOLD

(Fig. 7C). The success rate of ICM with this subset of 100 PDB

structures was not available, but its success rate with the entire

150 complexes was 45%. Jain docked the same 100 PDB com-

plexes using Surflex and its success rate was 54%10. SKATE’s

systematic sampling coupled with FRED-Opt-Score ranking was

successful in identifying a pose that was within 2.0 A RMSD of

the native structure as the best pose for 56% of the cases. This

result was obtained by using six initial ligand conformations,

one generated by Corina31 and five generated by Omega.17 The

five lowest energy Omega conformers were added to increase

ring diversity. SKATE does not perform ring sampling, if the

initial ligand conformation contains experimentally determined

ring conformation, the SKATE result for this set improved to

71% (Fig. 7C, SKATE*). SKATE’s systematic sampling was

anchored by H-bond anchor points and the ligand was allowed

to sample regions outside of this 5 A radius. The docking site

volume in SKATE is similar to that used by other docking pro-

grams.

Comparing results from different docking programs are not

always straightforward.27,28 Results depend on, by varying

degrees, receptor preparation, initial structure of the ligand,

docking site volume, and quality and composition of test sets.

Generous sharing of protein and ligand files by test set authors

has made it easier to do fair comparisons. In this work, when-

ever possible, we aimed for minimally-biased comparisons by

using conditions (described above) that were parallel to those

used in other docking programs. Receptor files were downloaded

from each test set’s respective websites and were used without

modification (other than file format conversion).

Bias, whether intentional or unintentional, is invariably intro-

duced in results reported by authors of docking programs. One

of the best available methods to compare docking program per-

formance is blind docking assessments like the community wide

Statistical Assessment of the Modeling of Proteins and Ligands

(SAMPL) experiment (http://sampl.eyesopen.com).

Cross Docking

The thymidine kinase data set from the comparative article of

Bissantz et al.24 and the cyclin-dependent kinase 2 data set from

Yang et al.25 were used to test the cross-docking performance of

SKATE. The TK set was originally used to quantitatively com-

pare the performance of GOLD, DOCK, and FlexX. Data on

this set are also available for Glide and Surflex. The TK struc-

ture used for docking was the deoxythymidine-bound structure

(PDB code 1KIM). Table T22 summarizes the top-scoring RMSD

values generated by the different docking programs for 10 thy-

midine kinase ligands. The ligand and receptor structures were

prepared as described in Bissantz et al. FRED-Opt-Score was

used to rank the poses generated by SKATE. Five of the 10

ligands were docked to the 1KIM structure with an RMSD of

less than 1.8 A. Another five failed to dock and their RMSD

values were between 3 and 4 A. Of the five failed cases,



Figure 7. Distribution of the RMSD values between the top-ranked

docking poses and the corresponding crystal structures in the Astex/

CDCC set (A), Surflex set (B), and Vertex set (C). RMSD values

were calculated on the coordinates of the heavy atoms of the

ligands. X-axis: RMSD cutoffs; Y-axis: percentage of top-ranked

docking poses within a given RMSD cutoff from the crystallo-

graphic pose.

COLOR



SKATE generated poses that were less than 2.0 A RMSD for

four ligands. However, FRED-Opt-Score failed to rank them as

top-scoring poses. The RMSD values of the best pose for ligands

hpt, hmtt, gcv, pcv, and acv were 0.35 A, 1.19 A, 2.11 A, 1.65 A,

and 1.37 A, respectively. As pointed out by Friesner et al.11,

ligands acv, gcv and pcv are purine-based ligands and do not fit

properly into the pyrimidine-based ligand site. All six docking

programs did not sufficiently sample receptor flexibility and there-

fore all failed to dock these three ligands. The cross-docking

results by SKATE are comparable to Glide, GOLD, and Surflex.

The CDK2 test set consists of 73 complexes and the ligands

were docked to a single CDK2 protein structure (PDB ID

2B54). The resolution of 2B54 is 1.85 A and is cocrystallized

with 6-(3,4-dihydroxybenzyl)-3-ethyl-1-(2,4,6-trichlorophenyl)-

1H-prrazolo[3,4-d]pyrimidin-4(5H)-one. The 2B54 structure was

selected to be the model receptor because it is the best-resolu-

tion structure with no missing residues or side-chain atoms. Two

sets of VDW scaling parameters were tested in docking the 73

ligands to 2B54. The default VDW scaling value for intermolec-

ular interactions is 0.9. A second set of parameters allows even

more VDW penetration by using a scaling value of 0.8. Reduc-

ing VDW radii is a technique docking programs can employ to

mimic receptor side-chain flexibility. Admittedly, this generates

poor mimicry of receptor flexibility, yet is nevertheless useful

until more advanced features are added to SKATE. To evaluate

sampling and scoring accuracy, we used heavy atom RMSD

from the native structure. To transform the reference coordinates

into the same global coordinates, 72 of the 73 complexes were

structurally aligned to 2B54 using pymol32 and ligands were

extracted and saved in the Tripos mol2 format. The sampling

results from using the two different VDW scaling parameters are

shown in FigureF8 8A. More permissive VDW parameters allow

for more VDW penetration; hence more receptor flexibility

result in improved sampling. SKATE was able to sample a pose

that was within 2 A RMSD of the native structure for 81% of

the ligands (Fig. 8A dotted curve). However, this level of VDW

scaling was not accommodated in FRED-Opt-Score. A low

RMSD pose will score poorly if there are severe VDW penetra-

tions. The percentage of top-scoring poses as a function of

RMSD is shown in Figure 8B. At an RMSD cutoff of 2.0 A

RMSD, the success rate was 38%. Scaling atomic VDW radii by

a factor of 0.8 improved sampling but a similar improvement

was not achieved in scoring. The percentage of top-scoring

ligand poses plotted as a function of RMSD threshold was simi-

lar for the two sets of VDW scaling parameters (Fig. 8B). In

terms of overall docking accuracy, there was no significant

advantage to using a VDW scaling value of 0.8. Thus, modifica-

tions to SKATE to systematically include receptor flexibility

using the same approach are under consideration.

Pitfalls in Complex Preparation

The Vertex data set was prepared by performing a constrained

minimization of the complexes using MacroModel and the



Table 2. Accuracy in Cross Docking of Thymidine Kinase Inhibitors to

the 1KIM site.a

Ligand

RMSD (A) of top-scoring pose

SurflexSKATEb Glide DOCK FlexX GOLD

dT 0.21 0.45 0.82 0.78 0.72 0.74

ahiu 0.61 0.54 1.16 0.88 1.63 0.87

mct 0.52 0.79 7.56 1.11 1.19 0.87

dhbt 1.74 0.68 2.02 3.65 0.93 0.96

idu 0.22 0.35 9.33 1.03 0.77 1.05

hmtt 3.24 2.83 9.62 13.30 2.33 1.78

hpt 4.03 1.58 1.02 4.18 0.49 1.90

acv 3.57 4.22 3.08 2.71 2.74 3.51

gcv 3.33 3.19 3.01 6.07 3.11 3.54

pcv 3.80 3.53 4.10 5.96 3.01 3.84

aData for DOCK, FlexX, and GOLD are taken from Bissantz et al.;24

data for Surflex are taken from Jain22; data for Glide are taken from

Friesner et al.11

bFRED-Opt-Score was used to rank the poses generated by SKATE.

Figure 8. (A) Cumulative proportion of best RMSD poses for the

CDK2 cross-docking set using two sets of VDW scaling parameters.

(B) Cumulative proportion of the RMSD between the top-ranked

poses and the native structure. FRED-Opt-Score was used to rank

the poses. The default intermolecular VDW scaling value was 0.9.

The CDK2 VDW scaling value was 0.8.



OPLS/AA force field.33,34 Heavy atoms were constrained to their

original position while hydrogen atoms were allowed to opti-

mize. While this alleviated poor contacts between software-

added hydrogen atoms, it could lead to artifacts where a hydro-

gen atom can bend out of plane to relieve steric interactions.

Shown in FigureF9 9 is an example where an aromatic hydrogen

was bent 25 degrees out of plane during the minimization step.

Hawkins et al. pointed out additional pitfalls in complex prepa-

ration and X-ray structure quality.28 However, not optimizing

software-added hydrogen atoms also has its problems. A proton

on the ligand penetrated the VDW surface of a proton atom on

a lysine side-chain in complex 1YGC of the Astex/CDCC set. In

this case, the poor contacts could have been alleviated by a

quick minimization.

Computational Time

Using SKATE, the average docking time per ligand-protein

hydrogen-bond pair was less than 5 min for ligands with six or

fewer rotatable bonds, and 10 min for ligands with 8 rotatable

bonds. Total docking time was proportional to the number of

possible hydrogen bonds that a ligand can form with the recep-

tor. For the Astex/CDCC set, the median docking time was 42

min and the average docking time was 98 min on a single CPU

(Pentium 4, 2.4 GHz) computer running Linux. SKATE allows

simple parallelization by submitting each possible hydrogen-

bond pairing to a different CPU in a computing cluster.

SKATE has not been optimized as it is still a prototype

under development to evaluate the separation of docking from

scoring. Limited optimization, however, should allow significant

reduction in computational time. Further speed improvement in

SKATE can be made by implementing look-ahead technologies

to further prune the combinatorial search tree.16,35 Knowledge

about distance constraints between pharmacophore points can

also be used to prune the search tree. Additional heuristics can

be applied to reduce the number of discrete torsions sampled.

Speed improvement will make SKATE more amenable to virtual

screening applications of large compound libraries for which it

is not appropriate in its current version.

Conclusions

We implemented a novel docking concept in SKATE that

decouples systematic sampling from scoring to improve overall

docking accuracy. SKATE’s systematic sampling coupled with

FRED’s optimization and scoring was comparable to commercially

available program across three large data sets. Systematic sam-

pling in SKATE was robust as tested by three large self-docking

test sets and two cross-docking test sets. The high-quality poses

generated by SKATE could be used to train scoring functions to

distinguish between near-native and poorly docked poses.

The problem of false negatives is often the root cause of

poor performance in docking programs. If a docking program

never samples near-native poses, then there is zero chance that a

scoring function can rank them as top-scoring poses. Unfortu-

nately, modern docking programs’ sampling methods are de-

pendent on scoring functions that, at best, approximate experi-

mental binding energies. The interdependence of sampling and

scoring makes it difficult to determine whether a sampling error

or a scoring error caused significant problems in a docking

experiment. SKATE breaks this dependence by systematically

sampling all sterically allowed poses of a ligand as constrained

by a receptor pocket. This work shows that improved sampling

contributed to docking accuracy.

An executable version of SKATE and the five test data sets are

available for download from http://www.ccb.wustl.edu/software.

Methods

An aggregate is defined as a set of atoms whose relative posi-

tions are invariant to rotational degrees of freedom.16 Atoms in

an aggregate could be directly bonded, have a 1–3 relationship

defined by a bond angle, be part of a ring system, or have bonds

between them conjugated by resonance. Table 1 lists the number

of rotatable bonds, sampled by SKATE, for the ligands in the

three self-docking test sets. Figure 2 illustrates how a simple mol-

ecule was divided into three aggregates. There are T11 aggre-

gates and T torsional degrees of freedom in a flexible molecule.

Sterically allowed conformations of a ligand are generated by

assembling its aggregates. Since the distance between two atoms

within an aggregate is constant, it is not necessary to check for

VDW clashes between atoms within the same aggregate.

In SKATE, sterically allowed poses of a ligand are con-

structed in a stepwise fashion by reassembling the aggregates

comprising the ligand. Starting with an initial aggregate that

contains an atom that forms a hydrogen bond with a receptor

atom, a second aggregate is added via the rotatable bond that

joins the two aggregates (Fig. 1). Some torsion values around

this shared rotatable bond will lead to VDW overlaps between

atoms in aggregate two and atoms in aggregate one, as well as

atoms in the receptor. It is extremely inefficient to assemble two



Figure 9. An aromatic proton in test case 13GS of the Vertex set

was bent out of plane by an optimization step in complex prepara-

tion. Heavy atoms in a complex were fixed while protons were

allowed to optimize. This proton (cyan) was bent out of plane by

25o to relieve steric overlap with a proton on residue Pro202 of the

receptor. [Color figure can be viewed in the online issue, which is

available at www.interscience.wiley.com.]



aggregates for a given torsion only to find out that it is a steri-

cally impossible conformation. Discriminant analysis solves this

problem by analytically calculating the range of sterically

allowed torsions within which two aggregates can be assembled

without steric overlap. The result is that only allowed torsions

are sampled. In theory, systematic sampling should find all steri-

cally allowed poses of a ligand. In practice, SKATE discretizes

the continuous conformational space and then uses adaptive

torsion sampling and radial sampling to ensure sufficient

sampling.35

Discriminant analysis was first applied to systematically

search the conformational hyperspace available to a flexible

molecule to define three-dimensional quantitative structure-activ-

ity relationships (3D-QSAR) and biological receptor mapping.36

In the construction of a molecule from stepwise addition of

aggregates, there are two sets of atoms to consider. First are

those in the sterically allowed partial molecule (set A) previ-

ously constructed. Second are those in the next aggregate (set B)

to be added to the existing partial molecule. Atoms in set B

must be checked against those in set A to find torsions that are

sterically allowed. Distance constraint equations are used ana-

lytically to determine the possible torsion ranges such that a

new aggregate can be added without steric overlap between

atoms in the new aggregate (set B) and the partial conformation

(set A). These equations, derived elsewhere,36 describe the vari-

able distance between any two atoms as a function of a single

torsion angle (x). The square of the interatomic distance

between aj and ai in FigureF10 10 is given by:

d2ijðxÞ ¼ d1 þ d2 cosðxÞ þ d3 sinðxÞ (1)

where coefficients d1, d2, and d3 are defined as follows:

d1 ¼ j s!j2 þ j v!j2 � 2ð s!� v!1Þ

d2 ¼ �2ð s!� v!2Þ

d3 ¼ �2ð s!� v!3Þ

v1, v2, and v3 are the three orthogonal components of the vector

v in Figure 10 where

v!¼ aj � ar

v!3 ¼ u!3 v!

v!2 ¼ u!3 v!3

v!1 ¼ v!� v!2

Equation (1) can be rewritten as

g2ijðxÞ ¼

ax2 þ bxþ c

1þ x2

where

a ¼ d1 � d2

b ¼ 2d3

c ¼ d1 þ d2

x ¼ tanx2

� �

Let cij be the sum of the VDW radii for atoms i and j, then

differential distance function d2ijðxÞ ¼ d2

ijðxÞ � c2ij is evaluated to

determine whether or not the two atoms are in contact. The dif-

ferential distance function can be converted to a quadratic form

d2ijðxÞ ¼

ða� c2ijÞx2 þ bxþ ðc� c2

ijÞÞ1þ x2

D ¼ b2 � 4ða� c2ijÞðc� c2

ijÞ

x ¼ �b�ffiffiffiffiDp

2a

x ¼ 2 tan�1ðxÞ

The resulting discriminant D can be used to determine if

there is a real or imaginary solution to d2ij(x). If D [ 0, then

d2ij(x) has real roots and the upper and lower bound values of

the torsional range (x) can be calculated from the above equa-



Figure 10. The variable distance between a fixed atom ai and a ro-

tatable atom aj is a function of a single torsional variable x. Atoms

ai, as and ar are rigid with respect to each other and they belong to

the sterically allowed conformation of a partially docked ligand.

Atoms as and ar forms the rotatable bond and determine the rotata-

tional axis. u is a unit vector along the axis of rotation. The tor-

sional variable of x is being evaluated by discriminant analysis to

determine the range of torsions where atom aj does not clash with

any atoms in the partial conformation.



tions. If D � 0, d2ij(x) has complex or real double degenerate

roots. For c� c2ij � 0, d2

ij(x) is positive for all values of ximplying that atom i and atom j never come in contact for any

torsional value of x. For c� c2ij � 0, d2

ij(x) is negative for all

values of x and there is no sterically allowed way to add the

new aggregate. In this case, the new partial conformation will

be discarded and this search branch of the tree truncated.

The distance constraint equations minimize the number of

pair-wise intramolecular and intermolecular distances that must

be evaluated in a systematic search. They prune the search tree

by analytically determining torsion ranges that result in sterically

allowed partial or complete conformers. The intersection of

allowed torsion ranges for every atom pair spanning a rotatable

bond results in discontinuous slices of torsion ranges in which a

new aggregate is added during the step-wise construction process.

The torsional ranges are discretized by adaptive sampling and ra-

dial sampling to ensure sufficient sampling.35 Adaptive sampling,

as opposed to uniform sampling, ensures that SKATE does not

over-sample or under-sample a torsional range. Radial sampling

determines the increment in degrees between two sampled torsions.

In SKATE, a rotation of an aggregate around its rotatable bond

displaces an atom in the aggregate by a maximum of 0.25 A.

SKATE pairs an H-bond donor of a receptor with an H-bond

acceptor of a ligand, and vice versa, to anchor systematic search.

In SKATE, three parameters are used to define a hydrogen

bond, the distance between the hydrogen atom and the acceptor

atom; the angle formed by the acceptor, hydrogen, and donating

atoms; the angle formed by the acceptor base, acceptor, and

hydrogen atoms. FigureF11 11 illustrates how SKATE initializes its

H-bond pairing and systematic search process. A receptor H-

bond donor is paired with a ligand H-bond acceptor. Rotation of

the N��H bond on the receptor determines the 3D coordinate of

the ligand acceptor atom. Using discriminant analysis, SKATE

quickly determines the allowed torsions of the N��H bond such

that the ligand acceptor atom does not clash with receptor

atoms. The next bond to be rotated is the H-bond between the

receptor and the ligand. This determines the allowed torsions of

the H-bond such that ligand atoms in the first aggregate do not

clash with the receptor atoms. The remaining aggregates are

then systematically searched by recursion. Sterically allowed

poses for a given ligand-receptor hydrogen-bond represent leaves

of a tree graph where nodes represent aggregates and edges rep-

resent discrete torsions of rotatable bonds (Fig. 1). SKATE trav-

els this tree using a depth first search approach as illustrated by

the following pseudo code.

Systematic Search Pseudo Code

MAIN( )

DOCK (receptor, ligand)

SEARCH (receptor, ligand, torsions, agg_idx)

SEARCH (receptor, ligand, torsions, agg_idx)

UPDATE (ligand, agg_idx)

VALIDATE(receptor, ligand, torsions, agg_idx)

for each allowed torsion of aggregate agg_idx

ROTATE (ligand, torsions)

if last aggregate

RECORD (ligand)

else

SEARCH (receptor, ligand, torsions, agg_idx11)

end if

end for

The DOCK procedure transforms the coordinates of a ligand

H-bond partner such that it forms a hydrogen bond with a recep-

tor partner. The resulting H-bond geometry is determined by a

set of geometric H-bond parameters.

The UPDATE procedure transforms the atoms in aggregate

agg_indx to be in the same local coordinates as the previously

searched aggregates and partially assembled molecule.

The VALIDATE procedure performs discriminant analysis to

find allowed torsions of the rotatable bond that connects aggre-

gate agg_indx with the previously searched aggregates of the

ligand. A list of allowed torsions is stored in the torsions data

structure.



Figure 11. Docking of a ligand to a receptor by pairing H-bonding partners. Rotatable bonds in the

ligand are searched systematically to find allowed torsions that generate a bound pose for further

evaluation. [Color figure can be viewed in the online issue, which is available at www.interscience.

wiley.com.]



The ROTATE procedure simply rotates an aggregate to

an allowed torsion that was calculated by the VALIDATE

procedure.

Due to inherent errors in X-ray structure determination, there

are often VDW clashes between ligand and receptor atoms in

crystal structures. We employed a VDW scaling factor to reduce

the VDW radii of protein and ligand atoms to ensure the repro-

duction of experimental structures.37 A general scaling factor of

0.95 is applied to ligand intramolecular interactions. A 1,4 scal-

ing factor of 0.87 is applied to ligand atoms in 1–4 relationships.

Intermolecular interactions are scaled by a factor of 0.9 and

hydrogen-bond interactions are scaled by a factor of 0.6.

Acknowledgments

The authors thank Dr. Chris Ho for providing C libraries to read

mol2 files and to build data structures. They thank Robert Yang

for sharing the CDK2 data set, Dr. Ajay Jain for sharing the

Surflex set and Vertex set, and Dr. Marcel Verdonk for sharing

the Astex/CDCC set.

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SKATE: Decoupling Systematic Sampling From Scoring · 2014. 10. 10. · SKATE: Decoupling Systematic Sampling From Scoring JIANWEN A. FENG, GARLAND R. MARSHALL Department of Biochemistry